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    LCM for 20, 24 and 45

    "Least Common Multiple of 3 Numbers" Calculator
    Least Common Multiple of
    ,
    and

    What's the Least Common Multiple (LCM) of 20, 24 and 45?

    Answer

    LCM of 20, 24 and 45 is
    360

    First common multiples: 360; 720; 1,080; …

    360 is divisible by all three: 360 ÷ 20 = 18, 360 ÷ 24 = 15, 360 ÷ 45 = 8 — and 18, 15 and 8 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/20 by 18 and of y/24 by 15 and of z/45 by 8.

    20 = 22 × 5

    24 = 23 × 3

    45 = 32 × 5

    Prime202445Highest power
    22223—23
    3—33232
    55—55

    — = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

    LCM = 23 × 32 × 5 = 360

    More with these numbers

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    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/20--24--45Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/20--24--45">What is the LCM of 20, 24 and 45? - Calculatio</a>Copy
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    What is the LCM of 20, 24 and 45? The LCM of 20, 24 and 45 is 360 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/20--24--45/generated.jpgCopy

    LCM Table

    1st2nd3rdLCM
    202430120
    2024313,720
    202432480
    2024331,320
    2024342,040
    202435840
    202436360
    2024374,440
    2024382,280
    2024391,560
    202440120
    2024414,920
    202442840
    2024435,160
    2024441,320
    202445360
    2024462,760
    2024475,640
    202448240
    2024495,880
    202450600
    2024512,040
    2024521,560
    2024536,360
    2024541,080
    2024551,320
    202456840
    2024572,280
    2024583,480
    2024597,080

    FAQ

    What's the Least Common Multiple (LCM) of 20, 24 and 45?

    LCM of 20, 24 and 45 is 360

    How to find the LCM of 20, 24 and 45 by prime factorization?

    Take every prime that appears in 20, 24 and 45 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

    Can you get the LCM of 20, 24 and 45 two numbers at a time?

    Yes. The LCM of 20 and 24 is 120, and the LCM of 120 and 45 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 360 divisible by 20, 24 and 45?

    Yes, and by definition it is the smallest positive integer that is: 360 ÷ 20, 360 ÷ 24 and 360 ÷ 45 all come out whole. Any other common multiple of 20, 24 and 45 is a multiple of 360.

    See Also